Question

In a quadrilateral PQRS, PQ = PS and RQ = Rs. If ∠50° and ∠R = 110°, find ∠PSR.

Answer 1

In ΔPQS,
PQ = PS
∴ ∠PQS = ∠PSQ
∠P + ∠PQS + ∠PSQ = 180°
50° + 2∠PQS = 180°
2∠PQS = 130°
∠PQS = 65° = ∠PSQ ......(i)
In ΔSRQ,
SR = RQ
∴ ∠RQS = ∠RSQ
∠R + ∠RQS + ∠RSQ = 180°
110° + 2∠RQS = 180°
2∠RQS = 70°
∠RQS = 35°  = ∠RSQ ......(ii)
Adding (i) and (ii)
∠PSQ + ∠RSQ = 65° + 35°
∠PSR = 100°.